Final answer:
The question is solved by setting up a system of equations based on the given information. Soccer's fixed cost (FCI) is calculated to be $46.58, and basketball's FCI, being $9.01 more, amounts to $55.59.
Step-by-step explanation:
The student is asking to determine the individual fixed costs (FCls) for basketball and soccer given their combined total and the fact that basketball's FCI is $9.01 more than soccer's. To find the FCls of each sport, we can set up a system of equations.
Let's assume the FCI for soccer is x dollars. Therefore, the FCI for basketball would be x + $9.01. Together, the total FCI for both sports was given as $102.17. So, we can write the following equation:
Soccer's FCI + Basketball's FCI = Total FCI
x + (x + $9.01) = $102.17
Combining like terms and solving for x yields:
2x + $9.01 = $102.17
2x = $102.17 - $9.01
2x = $93.16
x = $46.58
Thus, soccer's FCI is $46.58 and basketball's FCI, being $9.01 more, is $55.59.